\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)
\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{90}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{9.10}\)
\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+..+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=2.\frac{2}{5}=\frac{4}{5}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)
\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{90}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{9.10}\)
\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=\frac{4}{5}\)
\(\frac{1}{3}\)+\(\frac{1}{6}\)+\(\frac{1}{10}\)+\(\frac{1}{15}\)+........+\(\frac{1}{45}\)
=\(\frac{2}{6}\)+\(\frac{2}{12}\)+\(\frac{2}{20}\)+\(\frac{2}{30}\)+..........+\(\frac{2}{90}\)
=\(\frac{2}{2.3}\)+\(\frac{2}{3.4}\)+\(\frac{2}{4.5}\)+\(\frac{2}{5.6}\)+...........+\(\frac{2}{9.10}\)
=2.(\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+\(\frac{1}{4.5}\)+\(\frac{1}{5.6}\)+.........+\(\frac{1}{9.10}\))
=2.(\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{6}\)+.......+\(\frac{1}{9}\)-\(\frac{1}{10}\))
=2.(\(\frac{1}{2}\)-\(\frac{1}{10}\))
=2.\(\frac{2}{5}\)
=\(\frac{4}{5}\)
CHÕ CHẤM LÀ 1/21
